Topological susceptibility and fourth cumulant in a uniform magnetic field

TL;DR

This paper investigates how a background magnetic field influences topological properties of the QCD vacuum, revealing flavor-dependent enhancements and suppressions in topological susceptibility and cumulants using chiral perturbation theory.

Contribution

It provides a detailed comparison of topological susceptibility and cumulant behavior across different flavor scenarios in magnetic fields within chiral perturbation theory.

Findings

Topological susceptibility enhancement is larger in three-flavor $ ext{χ}$PT than in two-flavor.

Suppression of the fourth cumulant is comparable at low fields and weaker at higher fields in three-flavor $ ext{χ}$PT.

Critical magnetic fields for topological effects are significantly different across flavor scenarios.

Abstract

We study the topological susceptibility and fourth cumulant of the QCD vacuum in a background magnetic field using three-flavor chiral perturbation theory ($\chi$PT) for arbitrary quark masses and $n$-flavor $\chi$PT with degenerate quark masses. We find that the enhancement of the topological susceptibility is larger in the three-flavor $\chi$PT compared to two-flavor $\chi$PT. Additionally, in comparing the fourth cumulant, we find that its suppression is comparable for magnetic fields, $eH\lesssim 0.8m_{\pi}^{2}$, and weaker for larger magnetic fields in three-flavor $\chi$PT with its enhancement beginning at a significantly lower critical magnetic field compared to two-flavor $\chi$PT. We also find that the enhancement of the topological susceptibility in $n$-flavor $\chi$PT with degenerate quarks is significantly larger and the suppression of the topological cumulant significantly greater at weak fields with the critical magnetic field pushed out to larger magnetic fields compared to both two and three-flavor $\chi$PT.